Scalar Potentials: Their Gradient Fields and Visualization

Setting up the combined potential due to three point potentials as an example to visualize gradients, divergences, and curls

A field source located a distance 1 south of the origin

Sources located distance 1 at 30° and 150°:

Function that returns the two dimensional (x,y) gradient field of any function declared a function of two arguments:

Generalizing the function to any arguments:

The sum of three potentials:

f(x,y) visualization of the scalar potential:

Contour visualization of the three-hole potential

Created by Wolfram Mathematica 6.0  (21 September 2007)